It really is no more complicated than they wrote themselves into a corner so they changed Khan's motivation. It works because Shatner and Montalban chew enough scenery that you get lost in the performances.
You, sir, above all of us, have finally had the courage to say the truth. You've said that which some of us have only allowed ourselves to think. I take my hat off to you. My finest meats and cheeses are yours for the taking.
The story requires Khan scanning the area and beaming up Kirk,
But that won't work. It's end of story if that happens. What happened instead would be like Captain Ahab finally having Moby Dick in his sites for the kill and then saying, "Look! Over there! A school of red snapper. I'm hungry and I love red snapper. Helm, hard to port. Nets in the water, men. We eat, tonight!"
Of course, Khan's motivation conveniently changed back to being target fixated on Kirk after he found out Kirk "escaped." Joachim should've led a mutiny. Khan had Genesis. That was a game changer. Khan could've had anything he wanted with Genesis as a bargaining chip, including Kirk. If Khan had become crazed enough not to see that, and still wanted Kirk worse at that point, he still could've said, "Kirk I offer you a trade. Genesis for you." How could Kirk refuse? Superior intellect my ass.